Best-fit criterion within the context of likelihood maximization estimation

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This article presents an approach toward surface best-fit based on Bayesian inference statistics. The objective is to propose a best-fit criterion which integrates the distribution of points around the best-fit feature. This approach is used to guarantee a better estimate of the best-fit feature parameters. The best-fit criterion proposed in this article accounts for varied distributions that are not necessarily symmetric, such as those generated by turning and milling processes. It forms a generalization of least squares and enables the user to add information concerning the expected residual distribution shape. Therefore it provides the same results as the least squares method when the hypothesis of normal distribution is chosen. This article shows that using the proposed criterion will bring about a better estimate of the orientation of the best-fit feature and will lead to an evaluation of the form defect which is the closest to actual fact.